Block #1,573,767

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/6/2016, 2:42:03 PM · Difficulty 10.7097 · 5,241,248 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

8b6b88a5c63b3475415c65a8f7ac3d8ccd33d145097b58f2027c444b759fda97

View on Chainz ↗

Height

#1,573,767

Difficulty

10.709680

Transactions

Size

1015 B

Version

Bits

0ab5ad9e

Nonce

191,096,365

Timestamp

5/6/2016, 2:42:03 PM

Confirmations

5,241,248

Mined by

⛏️ P2SHAVjZGRaRaDLzZPN2EfvXjb3vxXxpxpz7pG

Merkle Root

08994b75981fc9b51368073b4d9bbbc0e3da879cfc8c8a891396a24140eac2ab

Transactions (2)

Coinbasef46379fb6a6b52…b0fe05c8f5d0e2

1 in → 1 out8.7100 XPM110 B

AVjZGRaR…xpxpz7pG

037f08c4785b72…566b2746ce37f1

5 in → 2 out71.8920 XPM814 B

ASDqmNbX…bPYzqGY7 AQcjeddP…AoqhXrhG

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.209 × 10⁹⁸(99-digit number)

12092624241241886194…23336402209444659199

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

1.209 × 10⁹⁸(99-digit number)

12092624241241886194…23336402209444659199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.209 × 10⁹⁸(99-digit number)

12092624241241886194…23336402209444659201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

2.418 × 10⁹⁸(99-digit number)

24185248482483772389…46672804418889318399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.418 × 10⁹⁸(99-digit number)

24185248482483772389…46672804418889318401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

4.837 × 10⁹⁸(99-digit number)

48370496964967544778…93345608837778636799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.837 × 10⁹⁸(99-digit number)

48370496964967544778…93345608837778636801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

9.674 × 10⁹⁸(99-digit number)

96740993929935089557…86691217675557273599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.674 × 10⁹⁸(99-digit number)

96740993929935089557…86691217675557273601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.934 × 10⁹⁹(100-digit number)

19348198785987017911…73382435351114547199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.934 × 10⁹⁹(100-digit number)

19348198785987017911…73382435351114547201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.869 × 10⁹⁹(100-digit number)

38696397571974035822…46764870702229094399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆

Rarity

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #1,573,767

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